A prefabricated modular unit construction bridging system in which all components are identical and interchangeable to meet any variation of span, width of roadway, number of lanes of traffic, and live load specification for any temporary, semi-permanent, or permanent bridge. The bridge is capable of being dismantled and the individual modular components used elsewhere to form a new bridge. The panels, when connected end-to-end to form the main load-bearing trusses of the bridge side girders, are of such a shape that they can be pinned together at their bottom chord level to support the standard cross-beams and modular deck units/bracing throughout the bridge and provide gaps between adjacent panels at their top chord level into which can be pinned other standard chord units of such a length calculated to eliminate entirely both the natural pin-hole deflection inherent in 2-pinned modular truss structures and the elastic deflection under dead load. Some or all of the elastic deflection due to live load may also be eliminated. Also, the same shaped basic panels can be up-turned to form a second story of panels in double story truss constructions. The bottom chords of the up-turned panels form the top chord of each truss of the side girders, and the bottom chord of the lower panels form the bottom chord of each truss of the side girders.